Many thanks for all the comments and suggestions. We are in SC so the point about hiking at altitude is noted and very helpful. The highest altitude I have been at for longer than a connecting flight is Breckenridge which is around 9600 and that was a challenge to walk the streets. We have 10 days, including travel days, so one concern is biting off more travel than we can chew during that time. We will also have our kids who are 15, 13 and 10 so we need to be sensitive to drive times between locations. Given time constraints we have decided to focus on areas in SLC, north to Bozeman and West to Cody. I don't think we will have time to make it to Glacier given how far out of the way it is relative to the other locations we will be seeing. Likewise, I would like to see Arches National park in Utah but it is somewhat out of the way and would require a full day it appears.
The Browning museum as well as the Cody Museum will be mandatory. The Teton's, SLC, Yellowstone, Beartooth and a stop in Montana will also be on the list as well. I would love to see Deadwood, Black Hills, Devils tower etc but I think it would be too far out of the way for us to cover in the time we have.

Any suggestions on places to stay or additional advice on routes are appreciated.